高、低阶精化有限元空间之间的守恒精确解转换
Conservative and accurate solution transfer between high-order and low-order refined finite element spaces
摘要：
在本文中，我们介绍了一般的转移算子之间的高阶和低阶的细化有限元空间，可用于耦合高阶和低阶的模拟。在低阶加细空间的自然约束下，证明了高阶到低阶和低阶到高阶线性映射都是保守的、保常数的和高阶精确的.虽然证明适用于仿射几何，数值实验表明，结果适用于更一般的弯曲和混合网格。这些运营商也有应用程序的背景下，粗化的解决方案定义的网格上的字段与ESTA细化。$H^1$有限元空间的传递算子需要全局耦合求解，为此，开发了鲁棒且高效的预条件子。我们提出了几个数值结果证实了我们的分析，并证明了新的映射的自适应网格细化和保守的多离散耦合的上下文中的效用。
英文摘要：
In this paper we introduce general transfer operators between high-order and low-order refined finite element spaces that can be used to couple high-order and low-order simulations. Under natural restrictions on the low-order refined space we prove that both the high-to-low-order and low-to-high-order linear mappings are conservative, constant preserving and high-order accurate. While the proofs apply to affine geometries, numerical experiments indicate that the results hold for more general curved and mixed meshes. These operators also have applications in the context of coarsening solution fields defined on meshes with nonconforming refinement. The transfer operators for $H^1$ finite element spaces require a globally coupled solve, for which robust and efficient preconditioners are developed. We present several numerical results confirming our analysis and demonstrate the utility of the new mappings in the context of adaptive mesh refinement and conservative multi-discretization coupling.
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